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Abstract

The solution of ordinary differential equations with constant coefficients by means of the L-transformation is accomplished very easily, since the L-transformation removes the differentiation, a transcendental operation, and an algebraic image equation is obtained. When the original equation contains derivatives with respect to two variables, say x and t, that is it represents a partial differential equation, then the L-transformation applied to the variable t will remove differentiation with respect to t, and the image equation is an ordinary differential equation, with the variable x. Obviously, for this purpose we must presume that t varies in the interval 0 ≦ t < ∞ the variable x may range in an interval which may be bounded or unbounded at one or both sides. Accordingly, we have in the xt-plane (see Fig. 48) as fundamental region of the partial differential equation either a half-strip or a quadrant or a half-plane.

Keywords

Partial Differential Equation Ordinary Differential Equation Singular Point Asymptotic Expansion Image Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1974

Authors and Affiliations

  • Gustav Doetsch
    • 1
  1. 1.Emeritus of MathematicsUniversity of FreiburgFreiburg i. Br.Germany

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